{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# ***Introduction to Radar Using Python and MATLAB***\n",
    "## Andy Harrison - Copyright (C) 2019 Artech House\n",
    "<br/>\n",
    "\n",
    "# Shnidman Approximation\n",
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Referring to Section 6.3.6, Shnidman  developed a set of equations, based on empirical data, for calculating the required signal-to-noise ratio for a specified probability of detection and probability of false alarm.  These equations are applicable to all of the Swerling target models for either a single pulse or the noncoherent integration of $N$ pulses. Shnidman's equation proceeds as follows.  First, the parameter $K$ is chosen based on the Swerling target type, then the parameter $\\alpha$ is chosen based on the number of pulses as (Equation 6.45)\n",
    "\n",
    "$$\n",
    "    K = \\begin{cases}\n",
    "    \\infty &\\text{Swerling 0}\\\\\n",
    "    1 &\\text{Swerling I}\\\\\n",
    "    N &\\text{Swerling II}\\\\\n",
    "    2 &\\text{Swerling III}\\\\\n",
    "    2N &\\text{Swerling IV}\n",
    "    \\end{cases}, \\hspace{0.4in}\n",
    "    \\alpha = \\begin{cases}\n",
    "    0 &N<40\\\\\n",
    "    \\frac{1}{4} &N\\ge40\n",
    "    \\end{cases}.\n",
    "$$\n",
    "\n",
    "Then the two parameters $\\eta$ and $X$ are computed from (Equation 6.46)\n",
    "\n",
    "$$\n",
    "    \\eta = \\sqrt{-0.8\\ln(4 P_{fa}(1-P_{fa}))} + \\text{sign}(P_d - 0.5)\\sqrt{-0.8\\ln(4 P_d(1-P_d))}\n",
    "$$\n",
    "\n",
    "and\n",
    "\n",
    "$$\n",
    "    X = \\eta\\Bigg[ \\eta + 2\\sqrt{\\frac{N}{2} + \\Big( \\alpha - \\frac{1}{4}\\Big)} \\,\\Bigg].\n",
    "$$\n",
    "\n",
    "The following constants are now computed (Equation 6.48 - 6.51)\n",
    "\n",
    "\\begin{align}\n",
    "    C_1 &= \\left( \\big[  (17.7006 P_d - 18.4496) P_d  + 14.5339\\big]P_d - 3.525 \\right) / K, \\\\ \\nonumber \\\\\n",
    "    C_2 &= \\frac{1}{K}\\bigg( \\exp\\big( 27.31 P_D - 25.14\\big) + \\big( P_d-0.8\\big) \\nonumber \\\\ &\\hspace{1.5in}\\times \\left[ 0.7\\ln\\left( \\frac{10^{-5}}{P_{fa}}\\right) + \\frac{(2N-20)}{80}\\right]\\bigg), \\\\ \\nonumber \\\\\n",
    "    C_{dB} &= \\begin{cases} C_1 &\\text{for}\\hspace{5pt}0.1\\le P_d \\le 0.872,\\\\[5pt] C_1 + C_2 &\\text{for}\\hspace{5pt}0.872\\le P_d \\le 0.99,\\end{cases} \\\\ \\nonumber \\\\\n",
    "    C &= 10^{(C_{dB}/10)}.\\nonumber \n",
    "\\end{align}\n",
    "\n",
    "Finally, the signal-to-noise ratio is (Equation 6.52)\n",
    "\n",
    "$$\n",
    "    {SNR} = 10\\log_{10}\\left(\\frac{C\\cdot X}{N}\\right) \\hspace{0.5in} \\text{(dB)}.\n",
    "$$\n",
    "\n",
    "Shnidman's equation has been shown to be accurate to within $0.5$ dB within the following bounds\n",
    "\n",
    "$$\n",
    "    0.1 \\le \\,P_d \\le 0.99, \\\\ \\nonumber \\\\\n",
    "    10^{-9} \\le \\,P_{fa} \\le 10^{-3}, \\\\ \\nonumber \\\\\n",
    "    1 \\le \\,N \\le 10.\n",
    "$$\n",
    "\n",
    "Shnidman's equation is valid for all five Swerling target types.  Shnidman's equation provides accurate results for first cut type of radar system calculations.\n",
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Begin by getting the library path"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import lib_path"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Set the start and end probability of detection"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "pd_start = 0.8\n",
    "\n",
    "pd_end = 0.99"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create the prbability of detection array using the `linspace` routine from `scipy`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from numpy import linspace\n",
    "\n",
    "\n",
    "pd_all = linspace(pd_start, pd_end, 200)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Set the probability of false alarm and the number_of_pulses"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "pfa = 1e-6\n",
    "\n",
    "number_of_pulses = 10"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Set the target type (Swerling 0 - Swerling 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "target_type = 'Swerling 2'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculate the error in the Shnidman approximation of signal to noise using the `single_pulse_snr` and `signal_to_noise` routines"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "from Libs.detection.shnidman import signal_to_noise\n",
    "from Libs.detection.non_coherent_integration import single_pulse_snr\n",
    "\n",
    "from numpy import log10\n",
    "\n",
    "error = [10.0 * log10(single_pulse_snr(p, pfa, number_of_pulses, target_type)) - signal_to_noise(p, pfa, number_of_pulses, target_type) for p in pd_all]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Display the error in the Shnidman approximation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1080x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "\n",
    "\n",
    "\n",
    "# Set the figure size\n",
    "\n",
    "plt.rcParams[\"figure.figsize\"] = (15, 10)\n",
    "\n",
    "\n",
    "\n",
    "# Display the results\n",
    "\n",
    "plt.plot(pd_all, error, '')\n",
    "\n",
    "\n",
    "\n",
    "# Set the plot title and labels\n",
    "\n",
    "plt.title('Shnidman\\'s Approximation', size=14)\n",
    "\n",
    "plt.xlabel('Probability of Detection', size=12)\n",
    "\n",
    "plt.ylabel('Signal to Noise Error (dB)', size=12)\n",
    "\n",
    "plt.ylim(-1, 1)\n",
    "\n",
    "\n",
    "\n",
    "# Set the tick label size\n",
    "\n",
    "plt.tick_params(labelsize=12)\n",
    "\n",
    "\n",
    "\n",
    "# Turn on the grid\n",
    "\n",
    "plt.grid(linestyle=':', linewidth=0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
